The People’s March, London, 23 June 2018. ‘What the destination looked like was never seriously explained; we only had the wildest dreams of the most extreme leave fantasists to go on.’
Photograph: Andy Rain/EPA

Hundreds of people of every political bent – and those with none at all – will gather at Newcastle’s Assembly Rooms tomorrow to demand the British people are granted their right to have the final say on any Brexit deal.

The Chequers Brexit compromise offers the worst of both worlds | Peter Mandelson

Our joint cause focuses on the political ascendancy. Polls are now consistently showing that more people support a vote than reject it – and the gap continues to grow. This is despite what we all know, that the nation is fed up with talking about Brexit – a word that the lexicon of British daily life cannot relinquish a moment too soon.

What we are urging is one last big push to secure the vote this country sorely needs, a vote that includes the option of a U-turn on Brexit.

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Is Brexit definitely going to happen? – video explainer

In 2016 the referendum result set us on the road to Brexit. What the destination looked like was never seriously explained; we only had the wildest dreams of the most extreme leave fantasists to go on.

Destination Brexit is still a matter of dispute, a subject of bitter disagreement even among the Conservative ideologues themselves. But as we draw closer, authoritative figures and bodies have become more convinced of the economic damage that will be wrought. Concerns have been raised over hospitals that will be shorn of medicines and staff, and preparations for the grim prospect of food shortages. What’s more, no one voted for the fudged Chequers compromise that the government finally cobbled together to get past a fractured cabinet.

David Cameron was willing to risk our country’s future on a referendum to settle the Conservative civil war over Europe that had raged for decades, a gamble that set us on the road to Brexit. Theresa May, and for that matter Jeremy Corbyn, must now have the courage to let the British people have the final say when we have some idea of what Brexit looks and feels like.

We must, though, learn from the 2016 referendum. Neither side covered themselves in glory, and talk of immediate Armageddon over a leave result was preposterous.

But some statements made by the leave campaign were misleading at best, and calculated lies at worst – the most infamous being the £350m Brexit dividend for the NHS, and that hundreds of thousands of immigrants from Turkey, which is far from even joining the EU, would somehow overwhelm the UK.

Those who were torn between the arguments rightly feel cheated by the mess the ​government has made of Brexit

What will be necessary for the People’s Vote is an independent arbiter to be appointed who can rule on whether such claims are correct and valid. Those found to be conjuring “facts” from thin air would be forced to publicly withdraw them and apologise. Moreover, now that we know there was Russian interference in the 2016 referendum, we must make sure this vote is fought cleanly, and is completely untainted.

Both sides would, of course, have to agree to this appointment.

We do not claim that people weren’t smart enough to make up their own minds about Brexit in 2016. They were, and the country was clearly divided fairly evenly.

But those who were torn between the arguments, whichever way they ended up voting, rightly feel cheated by the mess the government has made of Brexit. Any vote on the final deal – or, heaven forbid, no deal – is for them.

Those of us of differing political hues must work together to make sure we secure that vote. Tribal loyalties are being put to one side to fight for this common goal.

This is why we have written this article together: a Liberal Democrat whose political training began in the rough and tumble of 1970s Glasgow as a Labour councillor, and the only modern-day Conservative MP whose office boasted a picture of Edward Heath rather than Margaret Thatcher.

Conservative, Lib Dem, Labour, Green or whoever else wants to join us: we are in this together and will secure the People’s Vote you deserve.

• Vince Cable is leader of the Liberal Democrats; Neil Carmichael is president of Conservatives for a People’s Vote